2 Answers
2

Q-7 offsuit actually has a little higher than 50% chance of winning against a random hand. The hands closest to a return of 0% (return being probability of winning subtract the probability of losing) are Q-5 offsuit and J-5 suited. Q-5 offsuit has the worst positive return, at about 0.24%. J-5 suited is the closest starting hand to 0% return, at about -0.03%. So if you are playing against a random hand, then Q-5 offsuit would be the worst hand to play that is still "above average".

This table is useful if you want to see the rank order of the hands in a heads-up game.

Q7x or "The Computer Hand" is the median poker hand in Texas holdem. If you really want to analyse these things in more depth, I'd suggest getting Pokerstove. You can run all hand matchups with numerous competing opponents through the free software.